Elements of information theory
Elements of information theory
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Logistic Regression, AdaBoost and Bregman Distances
Machine Learning
Fast Nearest-Neighbor Search in Dissimilarity Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Index-driven similarity search in metric spaces (Survey Article)
ACM Transactions on Database Systems (TODS)
Fast construction of nets in low dimensional metrics, and their applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The skip quadtree: a simple dynamic data structure for multidimensional data
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Searching dynamic point sets in spaces with bounded doubling dimension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The black-box complexity of nearest-neighbor search
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
Clustering with Bregman Divergences
The Journal of Machine Learning Research
On the smallest enclosing information disk
Information Processing Letters
Fast nearest neighbor retrieval for bregman divergences
Proceedings of the 25th international conference on Machine learning
Coresets and approximate clustering for Bregman divergences
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Sided and symmetrized Bregman centroids
IEEE Transactions on Information Theory
Similarity search on Bregman divergence: towards non-metric indexing
Proceedings of the VLDB Endowment
Worst-Case and Smoothed Analysis of k-Means Clustering with Bregman Divergences
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Bregman vantage point trees for efficient nearest neighbor queries
ICME'09 Proceedings of the 2009 IEEE international conference on Multimedia and Expo
Bregman proximity search
Orthogonal Range Reporting in Three and Higher Dimensions
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Discrete & Computational Geometry
Geometric Approximation Algorithms
Geometric Approximation Algorithms
Efficient shape indexing using an information theoretic representation
CIVR'05 Proceedings of the 4th international conference on Image and Video Retrieval
Bregman clustering for separable instances
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
The Burbea-Rao and Bhattacharyya Centroids
IEEE Transactions on Information Theory
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In this paper, we give the first provably approximate nearest neighbor (ANN) algorithms for Bregman divergences over bounded domain.These process queries in O(log n) time for fixed dimensions.We also obtain poly-log n bounds for a more abstract class of distance measures (containing Bregman divergences) which satisfy certain structural properties. Both of these bounds apply to the regular asymmetric Bregman divergences as well as their symmetrized versions. Our first algorithm resolves a query for a d-dimensional (1+ε) ANN in O((log/n ε)O(d)) time and O (n logd-1 n) space and holds for generic μ-defective distance measures satisfying a reverse triangle inequality. Our second algorithm is more specific in analysis to the Bregman divergences and uses a further structural constant ,the maximum ratio of second derivatives over each dimension of our domain (c0). This allows us to locate a (1+ε)-ANN in O(log n) time and O(n) space, where there is a further (c0)d factor in the big-Oh for the query time.